Computing system



June 14, 1949. RAJCHMAN 2,473,444

COMPUTING SYSTEM Filed F613. 29, 1944 I s Sheets-Sheet 1 cowl/N6 77/555 IN VEN TOR.

June 14, 1949. J. A. RAJCHMAN COMPUTING SYSTEM 5 Shets-$heet 3 Filed Feb. 29, 1944,

Patented June 14, 1949 COMPUTING SYSTEM Jan-1 A Rajchman, Princeton; N. .11; assignor' to: RadiolGor-poration of America, arcorporationtof Delaware.

Application February=29, 19.44; S'eriaLNm. 524 475.

2 Claimsa (013235-4311 This: invention:.relates-.-to: computing: systems, such. asv aresutilizedatoeconvert sazvalue of .ia':vari-'.-- able to the value=: ot..a;i desired;.function.of. the; variable, and has for." itsaprincipal object the provisionzof an improved apparatus: and .method 0152:. operation; whereby" 1);. values:- of aa variable expressed 1 in: the; decimal T. system may; be come, vertedto. values of; a1.fi'irietiorri.of:thevariable expressed: in: the sameisystem; (2). valuesiofi a; variable, expressed :inttheesbiquinary' systern'rmay be. converted:torvaluess'of atfun'cti'on oti'th'ea'vari-e able expressed inthe-isamessystemor. (3) values expressedzin.onesnumerical system may Abe-readily converted .soa'. as tobeaexpressed in; another: nui-z mericall system;

The; presentiinventl'ont. isrrelated tot that; disclosed: a copendingzapplication Serialv No: 508,343;-.fi'ledf.. October; 30, 1943; now Patent: No: 2,428,811, which" is:- directed:v more. particularly to an apparatustfbr'iconverting 'valuessof a' vari able :expressedsinthe binary systemito values 01 a function" of:v the:- variable expressedin. the same system. This system is satisfactoryiwhere potentials: representative of thebinary values of the function 1 are to be utilized 1 directly in the control .of otli'er: apparatus; In some cases,'-however, a directindieation of values expressedin therde'crmale systemaisidesirable: This is realized by the presentiiriventiom In"- manyr computing-. devices,- \it': is desirable 1 to operate: with: numbers as opposed: to continuously; variable-physical quantities=such as voltage oncurrent; The :numb'ersupon whichthe com putatiomis made-areusually carriedon a system of conductors; some of which'liave-onedmnitmpotential and some oth'ers sh ave another defrnitea potential; usual decimal scale; theconductors? can' be? arranged in groups sofa" tens; eachrgroup: correspond in'g to a declmali pl'aoe andeach condutor' in" anyone: group: to: onei. oif theiten: decimal digits; If such. a: systemzis used; onezoiithe tenaconductors' in: any one groupj will :bei'of.:th'e-." petentialivi and; all .others: of: trier-potential: V2:

In .such;computing devices; 1551s? oftenid'eslrable to: generate .one. number. as r a function: of: one or. more others. The: functional relationship be.- tweenthe variable. and function isloften. given. 111'. terms of a table... linexample oilsuch. atable fer a one variablei function F. (XL is. glvenin. Table II Tbs represent numbers: in the TableI t 1 x F(X x... 724x 544.: 717.71 580 u 722.08 545" 717. 72 581 722; 38 546 7181 00 582 1 723. 72 547- 71s;-27. 583 725.21 54s 718:53 584' 727.53 549 718. 78 585 730119 550-. 719.02 586 1 734-37 7 551 719.25 587" 739198 552' 719.247 588:: 748.77 553= 719. 68 589. 757%82 554*. 719188 590" 769171 555%.. 9720506 I 591 781213 5567' 72023 I 592 798.53 557 "720139 593 815. 12 558 720154 594. 834471 559: 720. 68 595 4 857.13 560" 720. 81 596 893.15 561' 720.193 597 927:15 562 731.04 598 957.17 563 721.14 599 967373 564: J 7212 23 600 973257 565 721.31 601,- 981,18 566" 72738 602" 987:57 567. 7 21. '42 603 989.;63 568 721.47 604.. 991.37 569" 721151 605' 992.75 575. 721.54 606': 993.12. 571 721. 56 607-. 993. 98 572' 721757 608 994; 17 573 .721358 609- 994'. 25 574 721.60 610- i 994. 27 575 721163 611" 994. 26 576 7214 67 612 994; 25 577 721.72 613.. 994.24 578" 721:78 BM 99 1; 23 579: 721.88 615' 99422 If the various values are expressed in the-bl"- quinary system, the converting apparatus is "con siderably' simplified for the reason that-ten digits may berepresented" by seven potentials-- which arev divided" into 7 a group of five indicated as 0; 1, 2, 3; 4 and a'groupof two indicatedas A and Bi For every digit -of the value; one-conductor (if-each" group is excitedi The relation between the decimal and" biqui nary systems I is indicated by'the foll'owing TableII:

3 It is well known that the ten decimal system digits may be represented by four binary system digits. The relation between the two systems is shown by the following Table III:

Direct Decimal Decimal in Binary Notation Notation One or the other of twopotentials are applied to the vertical conductors in a manner to represent the successive digits of a number to be converted either to the value of a function or to the same value expressed in another numerical system. In the illustrated forms of the invention, a more positive potential of 340 volts generally is applied to a Vertical conductor which is to represent a digit and a more negative potential of 600 volts is applied to a vertical conductor which is to represent the absence of a digit. These voltages are established on the different vertical conductors through input tubes of the cathode follower type by switching their grid potentials to one or the other of the two indicated voltages or their equivalent.

When the number to be converted is expressed in the decimal system, a group of ten vertical conductors, numbered as 0, I, 2, 3, 4, 5, 6, I, 8, 9, is provided for each digital position of the number and only one of the conductors of each group is charged to the more positive potential. When the number to be converted is expressed in the biquinary system, two groups of conductors, numbered respectively 0, I, 2, 3, 4 and A, B, are provided for each digital position of the number and one conductor of each of the two roups is charged to the more positive potential. When the numbar to be converted is expressed in the binary system, the number of vertical conductors is equal to the number of the digital positions of the largest value to be converted and the vertical conductors corresponding to a digit one of the binary number are charged to the more positive potential While the other vertical conductors are charged to the more negative potential.

The horizontal conductors may be considered as corresponding to the diiferent values of a variable X, e. g. the diiferent numbers represented by potentials established on the vertical conductors as described above. Where the value of a variable is to be converted to the value of a function of the variable, these horizontal conductors are connected through one megohm resistors to the vertical conductors in such a way that the horizontal conductor representing a given value of the variable is charged to the more positive potential when and only when potentials representative of that value are applied to the input terminals of the vertical conductors. Where values expressed in one numerical system are to be converted to the same values expressed in another numerical system, the horizontal conductors are connected through one megohm resistors to the vertical conductors in a manner to make available at the output terminals of the horizontal conductors potentials representative of the converted numher as hereinafter explained.

In case the apparatus is to be utilized to convert the values of a variable to the values of a function of the variable, the horizontal conduc- 'tors discussed above are coupled to a second group of horizontal conductors which are interconnected with a second group of vertical conductors to form a function matrix. Potentials representative of the diiierent values of the function are derived from the output terminals of the second group of vertical conductors and indicated by any suitable means such as neon lamps or the like.

The invention will be better understood from the following description considered in connection with accompanying drawings and its scope is indicated by the appended claims.

Referring to the drawings:

Figure 1 is a wiring diagram of a generator which (1) is actuated by potentials representative of the various digits of a decimal system number expressing a selected value of a variable and (2) delivers at its output terminals potentials representative of the various digits of a decimal system number expressing the value of a function of the variable for such selected value,

Figure 2 is a wiring diagram showing the connections of one set of selector input, function matrix input and function matrix output tubes,

Figure 3 is a wiring diagram similar to that of Fig. 1 with the exception that it is modified to function in connection with decimal scale members having a biquinary notation and somewhat reduces the number of required parts,

Figures 4 and 5 illustrate certain details of an apparatus for converting a biquinary input to a decimal output,

Figures 6 and 7 illustrate an apparatus for converting a decimal input to a biquinary output,

Figure 8 illustrates an apparatus for converting a binary input to a decimal output, and

Figure 9 illustrates an apparatus for converting a decimal input to a binary output.

The function generating apparatus of Fig. 1

' includes a function matrix and a selector matrix each having a plurality of horizontal conductors. The horizontal conductors of the two matrices are coupled together through tubes each similar to the tube 20 of Fig. 2. The selector matrix also includes a plurality of vertical conductors which are shown as arranged in groups of ten, there being one of these groups for each digital position of the variable. To the lower or input ends of each of these vertical conductors of the selector matrix is connected an input tube similar to the tube 2| of Fig. 2. The function matrix also includes a plurality of vertical conductors which are shown as arranged in groups of ten, there being one such group for each digital position of the function of the variable. To the lower or output end of each of these vertical conductors of the function matrix is connected an output tube similar to the tube 22 of Fig. 2. These input, coupling and output tubes appear in Fig. 1

assmall circles. I "'Howthey operate' is -hereinailter explained in emu.

The flrorizon'tal "and "vertical conductors ot the selector "matrixare ixiterconnected- --so that suc- "cessive horizontal conductors represent successive ff-nnet-ion matrix *oorrespond to successive values or *thewariakhle. *Eaeh d'f 't'hes'e horizontal condud-tors is -=-'conn'ecte'd to the vertical conductors rof the function matrix so as to make available ait the lower en 'ds of the "vertical-conductors :po- *tentials representative e-1" the decimal system "number' -Which the'value o'f the fiunCtion for that "particularvalue of the variabl isexpresse'd. Thus the =l1'ori-zon'tal conductor representing a "value of 544 for' the variable is so 'connec'ted to the vertical oon'tluct'ors astoproduoe at-the output terminals of the function m'aiti ixpotentials representat-ive of a ifun'ction having a 'value of mum 5(see Table 1). "These-connections undicated by -=dots9 are each made througha one lmegohm resistor similar to the "resistor '24 or Fig.2.

The potentials representative of the selected value of the vai' iable'x are established on the *proper vertical oon'duetors of theselec'tor matrix by meansuif the-input" tl'ibes 1 I (see Fig. 2) which have their anodes grounded "and -=the'ir cathodes connectedtea- 800 veltIeadtli-rou'Qh a resistor '25. '-Wi't-h these 'connections, each-of these input tubes operates as a cathodefollower so that the vertical conductor to which it is connected is at a potential of -600 v. or -340 v. depending eon which of these --po'tentials is applied to "the -'control grid (if the input tube. When any =veritical-zconduotor does not *represent a digit of the selected value of -'=the "variable *X, its potential is established at 660 v. When suh'conduc'tor --does represent a digit (if the selected value of the "variable its potential is "established --at lrmtential of 340 v. to tu-be' ro'f the right hand vgroup of hipi-rt tubes, tothetube I of 'th'e cent'er group of input tubes and to the tribe 5 of the .lett han d group of input tubes. The-grid poten iti'als f al lthe other tubesof the three groups 1 a are maintained a't 600 v. "The r-e'sult' is that fine-horizontal 'cond-uctor 512 is at a more positive .potential 'Lthan "the other hor'izontal conductors or theiselectoramatrix.

iThismore :Tpositive ipoten'tia'l is applied through the vertical conductors, the resistors .23 land the .horizontal conductors to the control grids of "the icoupling "tubes ,;-2=0. -1example, a potential of about --3-10"v tmore positive than -600 vi) "is r applied to the grid :01 the-tube 20 tsee Fig. '2) *ethrough the vertical :conduct'or I reenter group) 2a resistor 23 andthe horizontal :conductor -512. 'Iihe :same :is true inf the vertical conductor of 1the2r1ght .:ha;nd :group and of conductor of rtheileft hand group, which, together with "the vertical "conductor -1 of the center *group, are @oonnected tosthe horizontal conductor 5 12. Since *the grids o'fthe coupli-ng tiibes *are --=each -*conmected to a difierent horizontal "conductor or the slec''ter matrial: ant! the'ir cathodes are m-aintainedat *34'0v., iit'rol1ows that theselected one or these "coupling "tubes will conduct and that all the other coupling "tubes will be biased off "(since the "grids (if these tubes are at 600 volts. "Itis fundamental that if a conductor is connected "through "equalresistances to three other conductors forcibly maintained at I different :poten't'ials -it assumes the average potential of these conductors. The *four possible cases are tabulated below:

(a) -34l), 340., 340 Average 3.40 340, -'3:4O, '600 Average '427 :(c) 3i40, 600, 'BUO Average -5l'3 "(6) '6D0, 4600, 600 Average 600 firmly-case tar) makes the .tube (20) conducting tsincethecath-ndes areat -'34'0.

FAIL the horizontal conductors 544 to H5 not the tunction matrix are at zero potential with :the exception of the one connected to the coupling .tube which is :not :biased -oiT. The one connected to the icoupling tube which .is not biased ofi tassumes !a potential of about -300 volts. The result is that all "the vertical sconductors of the Junction :matrix which are :CO11- mooted to this negatively charged horizontal conductor assume a negative potential with re- .spect tolallsthe other vertical wires of the r f-unctmn matrix and theoutput tubes '22 which have their grids connected to these negatively charged vertical conductors are biase'dsoff. This follows from the fact that the cathodes of all the output tubes "22 are grounded. For example, if "the horizontal conductor .51i2is connected to the coupling tube which is not biased off, the seven tube of 'the firstgroup .(the rig-ht hand one"), the fivetu'be of the second group, the one tube of the third group, the two ltube of the fourth group and the seven tube of the fifth-group are all biased "ofi. All the other output tubes 22 *areeonducting.

' For the purpose or indicating the value ofthe function (in the assumed case equal to 721.57) a neon lamp 26, or the equivalent, is connected 3 between "theanode of each tube and a v.

"terminal. ""Whenthe tube '22 is conducting, its anodeismorenegative due'to the potentialdrop of theresist'ori'l andthelamp 26 is unli'ghted, When thetube 22"i5not conducting, its potential "isfa't substantially the same potential as the -36Q v. lead "and the lamp 26 is lighted.

"Withthe selector and "function matrices conjnected as described "above, ever horizontal con- *duotor -"is connected to everyvertical conductor through many spurious-leakage paths. This "does mot 'in terf'ere "with the'operati'on of the selector :ma-trix because the degenerative drive of "the input tubes 24 maintains forcibly the desired j potentials of "the vertical -conduotors, nor do these spurious leakage paths or parasitic couplin'gs interi ere the operation -of the function matrix because I the ratio of the coupling re- Ffisistanee lone imegohm) to the driVing plate resistance *(30';0'00 ohms) is very high. he suggested in "the aforesaid copending "application Serial No. 508,343, these parasitic currents may the :min'imized :by ill) phase reversal on vertical :nondu'ctors having a num'ber of connections 'grea ter than mior (2) replacing :eahhoupling -"tube 20 by two "tubes arranged to-produce a del generativeidrive.

":zF lglure 3fillustrates a fu-notion generator which 'is 'simil-ar it but imonesim-ple than i that o'f F igs 1 and. 2 in ha a .is 'rbased' zon aibiquinarynotati'on '75 instead rifmidirect'denimalnotation. Bymeans of this notation, it is possible to express the ten digits by only seven potentials which are divided into one group of five, indicated by 0, 1, 2, 3 and 4, and one group of two, indicated by A and B. For every digit of the value of the variable, one conductor of the group of five and one conductor of the group of two is excited. The pattern of excitation is related to the decimal digits according to Table II generally discussed earlier in this disclosure.

The selector and function matrices for the biquinary system are constructed in a manner similar to those of the direct decimal system shown by Figs. 1 and 2. The connections of the various tubes and the values of all the resistances are the same. The proper connections between the horizontal and vertical conductors of the two matrices are indicated in Fig. 3 by dots. The vertical conductors of the selector matrix representing the digits of the selected value of the variable X are made more positive than other vertical conductors of the selector matrix in the same manner as that described above in connection with Figs. 1 and 2. For example, if the selected value of X is 572, the grids of the input tubes 2! connected to the vertical conductors 2 and A of the right hand group, 2 and B of the center group and 0 and B of the left hand group are all connected to the 340 v. terminal. This results in a more positive potential on the grid of the coupling tube 20 connected to the function matrix conductor 512 and biasing off of tubes 0 and B in the first group (right hand), I and A in the second group, 2 and A in the third group and 2 and B in the fourth group. Reference to Table II shows that a function having a value 721.5 is indicated. This agrees with Table I to the first decimal place. The values of additional decimal places, of course, may be derived by providing the function matrix with additional groups of vertical conductors properly connected to the horizontal conductors of this matrix. I

Certain parts of the apparatus of Figs. 1 and 2 and also those of Fig. 3 may be utilized for purposes other than those heretofore considered. For example, they may be utilized to convert from biquinary to decimal representation (see Figs. 4 and 5), to convert from a decimal representation to a biquinary representation (see Figs. 6 and 7), to convert from a binary representation to a decimal representation (see Fig. 8), or to convert from a decimal representation to a binary representation. (see Fig. 9).

It will be noted that Figs. 4 and 5 represent parts of a selector matrix similar to that of Fig. 3. In this case, the more positive potential (340 v.) and the more negative potential (600 v.) are applied selectively to the grids of the input tubes 2I-2I as previously indicated and potentials representative of the decimal output numbers corresponding to the biquinary input numbers are produced at terminals connected to the anodes of the tubes 20 as indicated by Fig. 5.

Figures 6 and 7 illustrate parts of a function matrix whereby decimal numbers are converted to the corresponding biquinary numbers. In this case, the more negative and more positive potentials are applied to the grids of the tubes 20 and the potentials representative of the biquinary numbers derived through the output tubes 22 and 22 are indicated by the, lamps 26 and 26.

'- Figures 8 and 9 show miniaturematrices suitable for converting binary numbers to corresponding decimal numbers and vice versa. As pointed out above in connection with Table III, the ten decimal digits may be represented in four binary orders. Fig. 8 illustrates an apparatus wherein potentials representative of a binary number are applied to the vertical row of potentials, and potentials representative of the corresponding decimal numbers are derived at the horizontal row of terminals all as pre viously described in connection with the preceding figures. Fig. 9 illustrates a similar apparatus for converting decimal numbers to corresponding binary numbers.

It is apparent that the present invention, like that of the aforesaid copending application Serial No. 508,343, is applicable to the derivation of functions depending on more than one variable such as F(X1, X2 X11). As explained in that application, all the systems of potentials of the variables X1, X2, etc., are applied to the input terminals of the selector matrix and the function corresponding to each set of values of the variables is established by proper connections between the horizontal and vertical conductors of the function matrix.

The basic features of the present invention are an improved apparatus and method of operation whereby (1) a value of a variable expressed in the decimal system may be converted to a value of a function of the variable expressed in the same system, (2) a value of a variable expressed in the biquinary system may be converted to a value of a function of the variable expressed in the same system, (3) values expressed in the decimal system may be converted to values ex pressed in the biquinary system or vice versa, and (4) values expressed in the decimal system may be converted to values expressed in the binary system or vice versa.

I claim as my invention:

1. The combination of a first set of conductors arranged in groups each including a number of conductors dependent on the number of digits in a predetermined numerical system, means for establishing on selected conductors of said groups potentials representative of the successive digits of a variable expressed in said numerical system, a second set of conductors, means connected between the conductors of said sets for applying a predetermined potential to a different one of the conductors of said second set in response to potentials representative of each different value of said variable, third and fourth sets of conductors,

I means interconnecting the conductors of said third and fourth sets in accordance with a predetermined function of said variable, means coupling the conductors of said second set to those of said third set, and means connected to the terminals of said fourth set of conductors for deriving potentials representative of different values of a function of said variable in response to shifting of said predetermined potential from one to another of said second set conductors.

2. The combination of a first set of conductors arranged in groups each including a number of conductors dependent on the number of digits in a predetermined numerical system, means for establishing on selected conductors of said groups potentials representative of the successive digits of a variable expressed in said numerical system, a second set of conductors, means connected between the conductors of said sets for applying a predetermined potential to a different one of the conductors of said second set in response to pc- 9 tentials representative of successive values of said variable, third and fourth sets of conductors, a plurality of electron discharge elements each having a control grid connected to a different one of said second set conductors and an anode connected to a different one of said third set conductors and to a source of potential through a resistor, resistive elements connected between the conductors of said third and fourth sets in accordance with a predetermined function of said variable, and means connected to the terminals of said fourth set conductors for deriving potentials representative of difierent values of said function in response to shifting of said predetermined potential from one to another of said second set conductors.

JAN A. RAJCHMAN.

REFERENCES CITED The following referenlces are of record in the file of this patent:

UNITED STATES PATENTS 

